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<title>Atlas software user guide -- (g,K)-modules</title>
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<h2>(g,K)-modules</h2>
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<i>Last updated: April 12, 2005</i>
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Let G be a connected reductive complex group, with a fixed
<a href="realforms.html">involution</a> &theta;; let K be the group of 
&theta;-fixed points in G, and <b>g</b>=Lie(G).
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The second major goal of the program, barely begun at this time, is to give 
access to the "local" aspects of the theory of (<b>g</b>,K)-modules for G
(by this, we mean questions that only involve representations at a fixed
infinitesimal character, say.) More precisely, we will deal with the following 
questions:
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<li><a href="blocks.html">blocks</a> of representations;</li>
<li>classifications of irreducible (<b>g</b>,K)-modules;</li>
<li>Kazhdan-Lusztig-Vogan polynomials;</li>
<li>K-multiplicities;</li>
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Eventually, we plan to treat these questions in full generality, i.e., for
arbitrary infinitesimal characters, possibly singular or non-integral. For
the near future, however, we will concentrate on the case of regular integral
infinitesimal character.
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